Maysan Mamoun has a dream that one day she and all other Saudi women will be able to play sport openly.

"I don't think this will last forever," she says, referring to the restrictions in place on Saudi women, who are not even allowed inside sports clubs, let alone to play for them. "We are pioneers. We will open doors."

Mamoun is the co-captain of the Green Team, a women's basketball team in Saudi Arabia. The only way the team can play is in private - they practice in the back garden of their other captain, Maysan Al Sowayigh. Al Sowayigh persuaded her parents to convert the space into a court for her so that the team would have somewhere to play.

Mamoun is speaking directly into a camera, filmed by a French documentary maker, Marian Lacombe. The interview forms part of Hey'Ya (which translates as 'Let's Go'), a free exhibition in central London that celebrates Arab women in sport, from amateurs to Olympians.

The videos complement dramatic large-scale photographs of more than 50 Arab sportswomen taken by Marian's sister, the photographer Brigitte Lacombe.

The Green Team is trying to convince families to let their daughters train with them, but says it's not an easy task in a country where sport is banned for girls in public schools.

"There was a sense of frustration among some of the women," says Brigitte, who travelled with her sister to Saudi Arabia, Qatar and Morocco to photograph and film the women. "But what is so remarkable is how they kept their focus. They will do what it takes to be able to participate in sport. I was humbled by their determination, smartness and dignity."

The Lacombe sisters were commissioned by the Qatar Museums Authority, which will be showing Hey'Ya in Doha next spring. Recently, Qatari authorities have been making an effort to prove to the International Olympics Committee that they are not discriminating or restricting women from participating in sports, as they prepare to bid for the 2024 Games. This year, Qatar is sending four women to the Olympics for the first time ever.

One of them is Noor Al Malki, a 17-year-old sprinter who is competing in the women's 100m. She has also been photographed and filmed for the exhibition. In one portrait, Al Malki is on the floor, stretching out in her sports gear, while in another, she poses side-on in the tight bandana she wears to cover her hair while running. In a video clip, Al Malki says she was too shy to run without her normal veil at first, but her brothers encouraged her. "They said just be strong."

Also featured in the exhibition are Hania Fouda, an Egyptian archer whose hands are painted with henna, and Feta Ahamada, an athlete from Comoros, a majority Muslim country off the coast of Mozambique who will also be competing in the women's 100m at the Olympics. Ahamada runs in a cropped athletic top and shorts. "If covering your body or your hair makes you feel comfortable, it's not a handicap," she says to the camera. "It's only sport. Everyone should do want they want."

Some of the women photographed are fully covered but most are not. "I want people to see the diversity of women in the Arab world. They are not all the same," says Lacombe, who spent seven months on the project.

Seventeen-year-old Reem Al Sharsani from Qatar missed out on an Olympics place this year in her sport, shooting, but has come to London for the start of the Games. She believes things are changing for young women of her generation; her older sister Yasmian plays golf and set up the Qatar Golf for Women club. Both were photographed by Lacombe.

"Before, women couldn't go out or do sports, but then everything changed when the Asian Games came to Qatar in 06. That's when women started realising it was possible to play too. Now I have a lot of support."

Yasmian, who wears a flowing black robe, agrees. "I'm so proud of all these women. I want to show the world we can do anything, even if we are covered. There will be no more barriers for us."

• Hey'Ya: Arab Women in Sport is at Sotheby's, 1-2 St George Street, London, until August 11; free entry; sothebys.com.